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  <div class="section" id="numpy-hamming">
<h1>numpy.hamming<a class="headerlink" href="#numpy-hamming" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.hamming">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">hamming</code><span class="sig-paren">(</span><em class="sig-param">M</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/function_base.py#L2860-L2957"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.hamming" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Hamming window.</p>
<p>The Hamming window is a taper formed by using a weighted cosine.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>M</strong><span class="classifier">int</span></dt><dd><p>Number of points in the output window. If zero or less, an
empty array is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p>The window, with the maximum value normalized to one (the value
one appears only if the number of samples is odd).</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="numpy.bartlett.html#numpy.bartlett" title="numpy.bartlett"><code class="xref py py-obj docutils literal notranslate"><span class="pre">bartlett</span></code></a>, <a class="reference internal" href="numpy.blackman.html#numpy.blackman" title="numpy.blackman"><code class="xref py py-obj docutils literal notranslate"><span class="pre">blackman</span></code></a>, <a class="reference internal" href="numpy.hanning.html#numpy.hanning" title="numpy.hanning"><code class="xref py py-obj docutils literal notranslate"><span class="pre">hanning</span></code></a>, <a class="reference internal" href="numpy.kaiser.html#numpy.kaiser" title="numpy.kaiser"><code class="xref py py-obj docutils literal notranslate"><span class="pre">kaiser</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The Hamming window is defined as</p>
<div class="math">
<p><img src="../../_images/math/f77408878f1ef4cb11c1e08ed8da2dcbb0e2a924.svg" alt="w(n) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1"/></p>
</div><p>The Hamming was named for R. W. Hamming, an associate of J. W. Tukey
and is described in Blackman and Tukey. It was recommended for
smoothing the truncated autocovariance function in the time domain.
Most references to the Hamming window come from the signal processing
literature, where it is used as one of many windowing functions for
smoothing values.  It is also known as an apodization (which means
“removing the foot”, i.e. smoothing discontinuities at the beginning
and end of the sampled signal) or tapering function.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r62552758bfb0-1"><span class="brackets">1</span></dt>
<dd><p>Blackman, R.B. and Tukey, J.W., (1958) The measurement of power
spectra, Dover Publications, New York.</p>
</dd>
<dt class="label" id="r62552758bfb0-2"><span class="brackets">2</span></dt>
<dd><p>E.R. Kanasewich, “Time Sequence Analysis in Geophysics”, The
University of Alberta Press, 1975, pp. 109-110.</p>
</dd>
<dt class="label" id="r62552758bfb0-3"><span class="brackets">3</span></dt>
<dd><p>Wikipedia, “Window function”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Window_function">https://en.wikipedia.org/wiki/Window_function</a></p>
</dd>
<dt class="label" id="r62552758bfb0-4"><span class="brackets">4</span></dt>
<dd><p>W.H. Press,  B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
“Numerical Recipes”, Cambridge University Press, 1986, page 425.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">hamming</span><span class="p">(</span><span class="mi">12</span><span class="p">)</span>
<span class="go">array([ 0.08      ,  0.15302337,  0.34890909,  0.60546483,  0.84123594, # may vary</span>
<span class="go">        0.98136677,  0.98136677,  0.84123594,  0.60546483,  0.34890909,</span>
<span class="go">        0.15302337,  0.08      ])</span>
</pre></div>
</div>
<p>Plot the window and the frequency response:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy.fft</span> <span class="kn">import</span> <span class="n">fft</span><span class="p">,</span> <span class="n">fftshift</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">window</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hamming</span><span class="p">(</span><span class="mi">51</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">window</span><span class="p">)</span>
<span class="go">[&lt;matplotlib.lines.Line2D object at 0x...&gt;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Hamming window&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 1.0, &#39;Hamming window&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Amplitude&quot;</span><span class="p">)</span>
<span class="go">Text(0, 0.5, &#39;Amplitude&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Sample&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 0, &#39;Sample&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../_images/numpy-hamming-1_00_00.png" src="../../_images/numpy-hamming-1_00_00.png" />
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="go">&lt;Figure size 640x480 with 0 Axes&gt;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">window</span><span class="p">,</span> <span class="mi">2048</span><span class="p">)</span> <span class="o">/</span> <span class="mf">25.5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">mag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">fftshift</span><span class="p">(</span><span class="n">A</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">response</span> <span class="o">=</span> <span class="mi">20</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="n">mag</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">response</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">response</span><span class="p">,</span> <span class="o">-</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">freq</span><span class="p">,</span> <span class="n">response</span><span class="p">)</span>
<span class="go">[&lt;matplotlib.lines.Line2D object at 0x...&gt;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Frequency response of Hamming window&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 1.0, &#39;Frequency response of Hamming window&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Magnitude [dB]&quot;</span><span class="p">)</span>
<span class="go">Text(0, 0.5, &#39;Magnitude [dB]&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Normalized frequency [cycles per sample]&quot;</span><span class="p">)</span>
<span class="go">Text(0.5, 0, &#39;Normalized frequency [cycles per sample]&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">&#39;tight&#39;</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../_images/numpy-hamming-1_01_00.png" src="../../_images/numpy-hamming-1_01_00.png" />
</div>
</dd></dl>

</div>


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